With the derived color-redshift relations, we can use our previously established
\(\chi ^2\) -minimization method to estimate the most probable photometric redshifts of quasars [1]}, [2]}.
Here the \(\chi ^2\)  is defined as (see [1]}):
\(\chi ^2=\sum _{ij}{\frac{[(m_{i,cz}-m_{j,cz})-(m_{i,observed}-m_{j,observed})]^2}{\sigma _{m_{i, observed}}^2+\sigma _{m_{j,observed}}^2}},\) 
